RMO 2023 Problem 1

Let $\mathbb{N}$ be the set of all positive integers and $S=\left\{(a, b, c, d) \in \mathbb{N}^4: a^2+b^2+c^2=d^2\right\}$ . Find the largest positive integer $m$ such that $m$ divides abcd for all $(a, b, c, d) \in S$ .